Abstract
A numerical study of the interaction between granular flow and an obstacle on an inclined plane is presented. A depth-averaged, two-dimensional Savage-Hutter-type model is used. The underlying differential equations are usually solved by finite difference. The model, which has been proved to perform well for steady granular flow, turns out to be inappropriate for the interaction between granular flow and obstacles. In this paper, the quality of the numerical solution is significantly improved by grid refinement. We make use of the Adaptive Mesh Refinement, where only local grid refinement around the obstacle is needed.
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References
M.J. Berger, P. Colella, Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 64–84 (1989)
M.J. Berger, J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53, 484–512 (1984)
M.-C. Chiou, Modelling dry granular avalanches past different obstructions. Ph.D. thesis, University of Darmstadt, Darmstadt, 2006
M.-C. Chiou, Y. Wang, K. Hutter, Influence of obstacles on rapid granular flows. Acta Mech. 175, 105–122 (2005)
J.M.N.T. Gray, M. Wieland, K. Hutter, Gravity driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. Lond. A 455, 1841–1874 (1999)
J.M.N.T. Gray, Y.-C. Tai, S. Noelle, Shock waves, dead zones and particle free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161–181 (2003)
R. Greve, T. Koch, K. Hutter, Unconfined flow of granular avalanches along a partly curved surface. Part I: theory. Proc. R. Soc. Lond. A 445, 399–413 (1994)
A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393 (1983)
K. Hutter, M. Siegel, S.B. Savage, Y. Nohguchi, Two-dimensional spreading of a granular avalanche down an inclined plane. Part I: theory. Acta Mech. 100, 37–68 (1993)
K.A. Lie, S. Noelle, An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions. J. Sci. Comp. 18, 69–80 (2003)
H. Nessyahu, E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87, 408–463 (1990)
H. Nessyahu, E. Tadmor, Nonoscillatory central for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19, 1892–1917 (1998)
S.P. Pudasaini, K. Hutter, Rapid shear flows of dry granular masses down curved and twisted channels. J. Fluid Mech. 495, 193–208 (2003)
S.B. Savage, K. Hutter, The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215 (1989)
S.B. Savage, K. Hutter, The dynamics of avalanches of granular materials from initiation to run-out. I. Analysis. Acta Mech. 86, 201–223 (1991)
Y.-C. Tai, J.M.N.T. Gray, K. Hutter, S. Noelle, Flow of dense avalanches past obstructions. Ann. Glaciol. 32, 281–284 (2001)
Y. Wang, K. Hutter, Comparison of numerical methods with respect to convectively-dominated problems. Int. J. Numer. Meth. Fluids 37, 721–745 (2001)
Y. Wang, K. Hutter, S.P. Pudasaini, The Savage-Hutter theory: a system of partial differential equations for avalanche flows of snow, debris and mud. J. Appl. Math. Mech. 84, 507–527 (2004)
Acknowledgements
We thank the Austrian Science Fund (FWF) for the financial support. We thank S. P. Pudasaini for fruitful discussions.
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Wawra, M., Wang, Y., Wu, W. (2011). Numerical Modelling of Interaction Between Snow Avalanche and Protective Structures. In: Bonelli, S., Dascalu, C., Nicot, F. (eds) Advances in Bifurcation and Degradation in Geomaterials. Springer Series in Geomechanics and Geoengineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1421-2_20
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DOI: https://doi.org/10.1007/978-94-007-1421-2_20
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